Department of the Interior, Bureau of Education, Bulletin, 1924, No. 18

**Preface**

Certain periods in the making of history have been deficient in contemporary chronicles. This is notably true in the history of American education during the eighteenth century. Such history presents lessons to the educator of a later generation. As we follow the growth of the American people from the status of settlers in a new country to that of a distinctive nation with its own life to provide for by training and education, we are led to an understanding of the American character and civilization of our own day. This understanding is necessary for all those who are engaged in the attempt to prepare boys and girls to take their places in the present social structure.

The history of education is made up in part of accounts of various subjects which have developed into courses of study. mathematics of some kind has always been included in such courses. In the American Colonies arithmetic was an important subject for practical reasons. It was needed for trade and commerce. With sailing vessels plying between Europe and America and the only means of communication with the "homeland," navigation and all the kinds of sailing that had to be put to daily use came to be a continuation of the course in arithmetic. Astronomical observations were an important feature in laying out a course at sea, and so astronomy is found in connection with arithmetic. Some elementary trigonometry, logarithms, and geometric constructions played a necessary part in the calculations incident to both navigation and astronomy. With this list the practical uses of mathematics in that day are exhausted.

It is the purpose of this study to show that algebra, another branch of mathematics, entered into the American education of the eighteenth century, and to show further that we must seek some other reason for its presence than a practical need for it.

**Table of Contents**

- Foreign influences leading to the introduction of algebra into American education

English influence

English algebra - Algebra at Harvard in 1730

Arithmetic notebooks

Algebra notebooks

Isaac Greenwood

Samuel Langdon

James Diman

Introduction of the Harvard manuscripts

Symbols

Topics

Subject matter of an advanced nature

Geometric problems

Sources of material

Algebra in the Harvard course - The notebook of a Princeton student
Philip Vickers Fithian, 1770-1772

Saunderson problems

Hill problems

William Churchill Houston, professor of mathematics - A mathematical notebook from the University of Pennsylvania

"Mathematica Compendia"

Robert Patterson, professor of mathematics - Manuscript material from miscellaneous sources

Manuscripts by Robert Brooke

"Practical Mathematics"

Nathaniel Bowditch

End of the notebook custom - Commencement theses

A commencement custom

Account of the custom of printing Latin commencement theses

Yale mathematical theses in 1718

Algebra theses in 1718

Samuel Johnson and algebra at Yale in 1718

Algebra theses at Harvard in 1721

Fluxions at Harvard and Yale - Mathematical theses of Harvard College

General account

Algebra theses - College reports and writings of professors and presidents

Harvard requirements

Hugh Jones, professor of mathematics at the College of William and Mary

Thomas Clap, president of Yale College

Records of the University of Pennsylvania

William Smith, provost of the University of Pennsylvania

Laws and orders at Kings College (Columbia University) - Evidence of the use of foreign textbooks

Scarcity of printed books

The Young Mathematician's Guide, John Ward

The Elements of Algebra, Nathaniel Hammond

A Treatise of Algebra, Thomas Simpson - The first books containing algebra published in the new world

A Mexican algebra

A Dutch algebra—Arithmetica of Cyffer-Konst

Pieter Venama - Eighteenth century nooks on algebra by American authors

Algebra in the work of Nicolas Pike

The American Youth. Consider and John Sterry - Algebra and advertisements

Algebra in the public press

Private tutors and schoolmasters

Solutions of algebra problems

Sale of algebra books - Summary

A chronological list of American algebra textbooks to 1820

Bibliography